Gordon, 43, was excluded from last year's race despite finishing fifth while racing under appeal following a row over a tyre inflation system on his car.
Preliminary checks by Dakar organisers have found the Hummer to comply with the 2013 regulations.
The Dakar Rally takes place from January 5-20. It begins in Lima, Peru and ends in Chile after crossing the Andes into Argentina.
Rival Stephane Peterhansel, a 10-times winner of the endurance rally - six times in the motorcycle class and four in a car - said Gordon was not welcome.
"This is a born cheat," he told AFP. "We're here to compete, not to show off; this is not the circus, even if it pleases the audience.
"We must fight on equal terms. Robby Gordon must comply with the rules. If this is the case, it is welcome. Otherwise... [not]."
Gordon's best finish on the rally is third in 2009, the first year it was moved to South America for safety reasons.
- Sports & Recreation
- Motor Rallying
- Robby Gordon